Question

A quality control inspector has drawn a sample of 12 light bulbs from a recent production lot. If the number of defective bulbs is 1 or less the lot passes inspection. Suppose 10% of the bulbs in the lot are defective. What is the probability that the lot will pass inspection

Answer 1

Answer:

90 percent

Step-by-step explanation:

100% - 10% = 90%

Answer 2

The Probability of passing the inspection will be 0.2426.

What is probability ?

The probability is defined as the ratio of possible number of outcome to the total number of outcome

We have,

And,

If the number of defective bulbs is 1 or less the lot passes inspection.

So,

According to the question,

Let,

Defective bulbs probability (p) = 10% = 0.1

Non defective bulbs probability  (q) = 100 – 10 = 90% =0.9

n = Sample of light bulb = 12

x = defective bulbs

Now,

If 10% of the bulbs in the lot are defective,

i.e. 12 * 10% = 1.2

Then,

x = defective bulbs = 1.2

Now,

Probability Binomial Distribution of Probability formula,

i.e. $^{n} C_{r}\ * \ p^x \ * \ q^{n-x}$

So,

Probability = $^{12} C_{1.2}\ * \ 0.1^{1.2} \ * \ 0.9^{12-1.2}$

On solving we get,

Probability = 12 * 0.02 = 0.2426

Hence, we can say that the Probability of passing the inspection will be 0.2426.

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